Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #423 |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,5,4)(10,12,14,13)(11,15,16,17);(6,7,8,9);(2,3,4,5)(7,9)(10,11,13,15,14,16,12,17)Polycyclic presentation:
2^6,5|a^2=d,b^2=e,c^2=f,d^2=f,b^a=be,c^a=cf,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598592, #10598594, #10598597, … |
| maximal normal subgroup of | #10598592, #10598594, #10598597, … |
| maximal quotient of | #10603787, #10603798, #10603816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1019);